The SPH method for simulating a viscoelastic drop impact and spreading on an inclined plate

Abstract

In the present work, the phenomenon of an Oldroyd-B drop impact and spreading on an inclined rigid plate at low impact angles is simulated numerically using the smoothed particle hydrodynamics (SPH) method. In order to remove the unphysical phenomenon of fracture and particle clustering in fluid stretching which is the so-called tensile instability, an artificial stress term is employed which has been successfully proposed in simulations of elastic solids. Particularly, the effects of surface inclination and the different regimes of drop impact and spreading on an inclined surface are investigated. The numerical results show the capability of the proposed scheme in handing the unsteady viscoelastic free surface flows. All numerical results of using the SPH method are in agreement with the available data.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

“…[11,17,28,37]. Tomé and McKee [35] performed a series of numerical experiments on this problem and showed that a 2D Newtonian jet will buckle if conditions Re < 0.56 and H/D > 8.8 are both satisfied.…”

“…3 and 4 display the width of the Newtonian and Oldroyd-B fluid drops, respectively, obtained using the proposed method and in previous works [11,17,28,37] as function of the dimensionless time t = t ⁄ U/L. In order to study the convergence of the numerical method with mesh refinement, we simulated these problems using Fig.…”

“…In the context of the Marker-And-Cell (MAC) method, the authors solved the Navier-Stokes equations and the constitutive law of an Oldroyd-B fluid by a projection method employing the full free surface stress conditions. The results obtained by Tomé and co-authors have been used to study the qualitative behavior of the simulations obtained by SPH methods, as for example in [11,17,28]. Another numerical investigation of drop impact using grid-based scheme was reported by Lunkad et al [20], using the volume of fluid (VOF) method.…”

“…In this context, Fang et al [11] studied the simulation of falling drops of an Oldroyd-B fluid while Rafiee et al [28] extended the incompressible SPH method for solving these phenomena using non-Newtonian models. More recently, Jiang et al [17] used the SPH method and presented a scheme that adds an artificial stress term to remove the unphysical characteristics of fracture and particle clustering in regions of fluid stretching. To assess the performance of their method, the authors simulated the viscoelastic drop impact and spreading over an inclined rigid surface.…”

Numerical study of the square-root conformation tensor formulation for confined and free-surface viscoelastic fluid flows

“…Figure 9 illustrates the drop shape and u-velocity field for different phases of the transient motions for Wi = λU /D = 1, where U is the initial velocity of the drop at height H, and D is the initial diameter of the drop. Typical difficulties in this simulation are the numerical instability for highly elastic flows in following the large deformation of the interface between liquid and air making the time-dependent impacting drop problem a popular benchmark for free surface flows of viscoelastic fluids [51][52][53][54]. However, the literature is scarce for high-Weissenberg number flows due to the inherent numerical difficulties.…”